In the past, in order to correct for deterioration from hand movements during capture of an image, processing was performed for restoring an image free from hand movements by means of actuation of an optical lens or subjecting a captured image to processing. When an image is restored through image processing, a deterioration in the image can be expressed asG=HF+N, provided that an original image is taken as F, a deterioration function as H, addition noise as N, and a deteriorated image as G. Consequently, at the time of restoration of an image, an equation of F=(G−N)/H is solved. When the size of the image is defined as M×N, the deterioration function H comes to a matrix of a size (M×N)×(M×N), and difficulty is encountered in carrying out actual computation. For this reason, there have been proposed various methods; namely, a method for converting a deterioration function into a diagonal matrix by means of Fourier transform and performing computation through use of the diagonal matrix, a technique for carrying out iterative operations of a steepest-descent method in an image space, and the like. In addition to including the steepest-descent method, examples of the iterative technique also include a moment method, a corrected moment method, a conjugate gradient method, and the like.
Japanese Patent Publication Laid-Open No. 2002-288653 and “New Edition of Image Analysis Handbook” (under general editorship of Mikio TAKAGI, University of Tokyo Press, September 2004) provide descriptions of a residue being computed every iteration when an image is restored by means of the iterative technique and iterative computation being determined to converge when the rate of a change in a previous residue and the rate of a change in a current residue have been the threshold value or less.
However, according to the steepest-descent method, convergence of iterative computation becomes slow in the neighborhood of an optimum solution. In order to acquire sufficient image quality, a large number of iterations must be performed.
The moment method and the corrected moment method need large memory capacity, because previous updated vectors must be retained.
The conjugate gradient method is considered to be an iterative method which effects convergence at the highest speed. However, memory capacity increases for the same reason.
The steepest-descent method will be described hereunder.